2018/07/20 by Pachon, Angelica, Polito, Federico, Ricciuti, Costantino · 1 citation
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1807.07932
In the last years, many authors studied a class of continuous time semi-Markov processes obtained by time-changing Markov processes by hitting times of independent subordinators. Such processes are governed by integro-differential convolution equations of generalized fractional type. The aim of this paper is to develop the discrete-time version of such a theory. We show that a class of discrete-time semi-Markov chains can be seen as time-changed Markov chains and we obtain governing convolution type equations. Such processes converge weakly to those in continuous time under suitable scaling limits.